Computerized Tomography and Reproducing Kernels

arXiv:2311.07465v2 Announce Type: replace-cross
Abstract: The X-ray transform is one of the most fundamental integral operators in image processing and reconstruction. In this article, we revisit the formalism of the X-ray transform by considering it as an operator between Reproducing Kernel Hilbert Spaces (RKHS). Within this framework, the X-ray transform can be viewed as a natural analogue of Euclidean projection. The RKHS framework considerably simplifies projection image interpolation, and leads to an analogue of the celebrated representer theorem for the …

abstract article arxiv framework fundamental image image processing integral kernel math.fa math.st operators processing ray replace spaces stat.ml stat.th type x-ray